2019/04/30 by Olivia Dumitrescu, Dumitrescu, Olivia, Nathan Priddis +1
Mathematics · #14C17 #14C20 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1905.00074
openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce and study divisorial (i) classes for the blow up of projective space in several points for i=-1,0 and 1. We generalize Noether's inequality, and we prove that all divisorial (i) classes are in bijective correspondence with the orbit of the Weyl group action on one exceptional divisor following Nagata's original approach. Moreover, we prove that the irreducibility condition from the definition of divisorial (i) classes can be replaced by the numerical condition of having positive intersection with all divisorial (i) classes of smaller degree via the Mukai pairing.